Find the vector equation of a line passing through the point (2\ha | Filo
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Class 12

Math

3D Geometry

Three Dimensional Geometry

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Find the vector equation of a line passing through the point and perpendicular to the plane .
Also, find the point of intersection of this line and the plane.

Solution:
Clearly, the required line passes through the point and is parallel to the normal of the given plane, which is .
So, the required vector equation is
.

The Cartesian equation of the line is .
A general point on this line is .

For same particular value of let the line cut the plane .
Then,

required point of intersection of the line and plane is
, i.e., .
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